Angles of elevation of pole are 60° and 45° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& \text{Height}\text{of}\text{pole}=PQ\\ & \tan 60^{\circ }=\sqrt{3}=\frac{PQ}{m}\\ & \tan 45^{\circ }=1=\frac{PQ}{n}\\ & \text{Multiply}\text{both}\text{equations}\\ & \sqrt{3}\times 1=\frac{PQ}{m}\times \frac{PQ}{n}\\ & \therefore PQ=\sqrt{mn\sqrt{3}}\text{units}\end{array}$$